/// <summary>Gets the value of the integral \int_a^b f(x) dx.
/// </summary>
/// <param name="lowerBound">The lower bound.</param>
/// <param name="upperBound">The upper bound.</param>
/// <returns>The value of \int_a^b f(x) dx.</returns>
/// <remarks>The arguments must be elements of the domain of definition, represented by <see cref="IRealValuedCurve.LowerBound"/> and <see cref="IRealValuedCurve.UpperBound"/> of the encapsulated <see cref="ICurveDataFitting"/> object.</remarks>
public double GetIntegral(double lowerBound, double upperBound)
{
if (UpdateRequested == true)
{
Update();
}
int leftGridIndex = GridPointArguments.BinarySearch(0, GridPointCount, lowerBound);
int rightGridIndex = GridPointArguments.BinarySearch(0, GridPointCount, upperBound);
if ((leftGridIndex >= 0) && (rightGridIndex >= 0))
{
return(m_Cache[rightGridIndex] - m_Cache[leftGridIndex]); // \int_{t_j}^{t_k} f(x) dx = \int_{t_0}^{t_k} f(x) dx - \int_{t_0}^{t_j} f(x) dx
}
else if (leftGridIndex < 0)
{
int previousLeftGridIndex = (~leftGridIndex) - 1; // previous grid point, i.e. smaller than the lower bound
var value = CurveDataFitting.GetIntegral(lowerBound, Math.Min(upperBound, GridPointArguments[previousLeftGridIndex + 1]), previousLeftGridIndex);
if (leftGridIndex != rightGridIndex) // lower and upper bound are not in the same interval [t_j, t_{j+1}]
{
if (rightGridIndex >= 0)
{
value += (m_Cache[rightGridIndex] - m_Cache[previousLeftGridIndex + 1]);
}
else
{
rightGridIndex = (~rightGridIndex) - 1; // previous grid point, i.e. smaller than the upper bound
var stepValue = CurveDataFitting.GetIntegral(Math.Max(lowerBound, GridPointArguments[rightGridIndex]), upperBound, rightGridIndex);
value += stepValue + (m_Cache[rightGridIndex] - m_Cache[previousLeftGridIndex + 1]);
}
}
return(value);
}
else // lower bound is a grid point and the upper bound is not a grid point
{
rightGridIndex = (~rightGridIndex) - 1; // previous grid point, i.e. smaller than the upper bound
var stepValue = CurveDataFitting.GetIntegral(Math.Max(lowerBound, GridPointArguments[rightGridIndex]), upperBound, rightGridIndex);
return(stepValue + (m_Cache[rightGridIndex] - m_Cache[leftGridIndex]));
}
}
/// <summary>Updates the internal cache.
/// </summary>
private void Update()
{
ArrayMemory.Reallocate(ref m_Cache, GridPointCount, pufferSize: 5);
var cumIntegralValue = m_Cache[0] = 0.0;
var lowerBound = GridPointArguments[0];
for (int k = 1; k < GridPointCount; k++)
{
var upperBound = GridPointArguments[k];
var upperGridPointValue = GridPointValues[k];
cumIntegralValue += CurveDataFitting.GetIntegral(lowerBound, upperBound, k - 1);
m_Cache[k] = cumIntegralValue;
/* prepare for next loop: */
lowerBound = upperBound;
}
UpdateRequested = false;
}
